Acoustics for Engineers

Acoustics for Engineers Ning Xiang Jens Blauert • Acoustics for Engineers Troy Lectures Third Edition 123 Ning Xiang Program in Architectural Acoustics Rensselaer Polytechnic Institute (RPI) Troy, NY, USA Jens Blauert Institute of Communication Acoustics Ruhr-Universität Bochum (RUB) Bochum, Germany ISBN 978-3-662-63341-0 ISBN 978-3-662-63342-7 https://doi.org/10.1007/978-3-662-63342-7 (eBook) Jointly published with ASA Press 1st & 2nd editions: © Springer-Verlag Berlin Heidelberg 2008, 2009 3rd edition: © Springer-Verlag GmbH Germany, part of Springer Nature 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany The ASA Press ASA Press, which represents a collaboration between the Acoustical Society of America and Springer Nature, is dedicated to encouraging the publication of important new books as well as the distribution of classic titles in acoustics. These titles, published under a dual ASA Press/Springer imprint, are intended to reflect the full range of research in acoustics. ASA Press titles can include all types of books that Springer publishes, and may appear in any appropriate Springer book series. Editorial Board Mark F. Hamilton (Chair), University of Texas at Austin James Cottingham, Coe College Timothy F. Duda, Woods Hole Oceanographic Institution Robin Glosemeyer Petrone, Threshold Acoustics William M. Hartmann (Ex Officio), Michigan State University Darlene R. Ketten, Boston University James F. Lynch (Ex Officio), Woods Hole Oceanographic Institution Philip L. Marston, Washington State University Arthur N. Popper (Ex Officio), University of Maryland Christine H. Shadle, Haskins Laboratories G. Christopher Stecker, Boys Town National Research Hospital Stephen C. Thompson, The Pennsylvania State University Ning Xiang, Rensselaer Polytechnic Institute The Acoustical Society of America On 27 December 1928 a group of scientists and engineers met at Bell Telephone Laboratories in New York City to discuss organizing a society dedicated to the field of acoustics. Plans developed rapidly, and the Acoustical Society of America (ASA) held its first meeting on 10–11 May 1929 with a charter membership of about 450. Today, ASA has a worldwide membership of about 7000. The scope of this new society incorporated a broad range of technical areas that continues to be reflected in ASA’s present-day endeavors. Today, ASA serves the interests of its members and the acoustics community in all branches of acoustics, both theoretical and applied. To achieve this goal, ASA has established Technical Committees charged with keeping abreast of the developments and needs of membership in specialized fields, as well as identifying new ones as they develop. The Technical Committees include acoustical oceanography, animal bioacoustics, architectural acoustics, biomedical acoustics, engineering acoustics, musical acoustics, noise, physical acoustics, psychological and physiological acoustics, signal processing in acoustics, speech communication, structural acoustics and vibration, and underwater acoustics. This diversity is one of the Society’s unique and strongest assets since it so strongly fosters and encourages cross-disciplinary learning, collaboration, and interactions. ASA publications and meetings incorporate the diversity of these Technical Committees. In particular, publications play a major role in the Society. The Journal of the Acoustical Society of America (JASA) includes contributed papers and patent reviews. JASA Express Letters (JASA-EL) and Proceedings of Meetings on Acoustics (POMA) are online, open-access publications, offering rapid publication. Acoustics Today, published quarterly, is a popular open-access magazine. Other key features of ASA’s publishing program include books, reprints of classic acoustics texts, and videos. ASA’s biannual meetings offer opportunities for attendees to share information, with strong support throughout the career continuum, from students to retirees. Meetings incorporate many opportunities for vii viii The Acoustical Society of America professional and social interactions, and attendees find the personal contacts a rewarding experience. These experiences result in building a robust network of fellow scientists and engineers, many of whom become lifelong friends and colleagues. From the Society’s inception, members recognized the importance of developing acoustical standards with a focus on terminology, measurement procedures, and criteria for determining the effects of noise and vibration. The ASA Standards Program serves as the Secretariat for four American National Standards Institute Committees and provides administrative support for several international standards committees. Throughout its history to present day, ASA’s strength resides in attracting the interest and commitment of scholars devoted to promoting the knowledge and practical applications of acoustics. The unselfish activity of these individuals in the development of the Society is largely responsible for ASA’s growth and present stature. Preface This book provides the material for an introductory course in engineering acoustics for students with basic knowledge of mathematics. The contents are based on extensive teaching experience at the university level. Under the guidance of an academic teacher, the book is sufficient as the sole textbook for the subject. Each chapter deals with a well-defined topic and represents the material for a two-hour lecture. The chapters alternate between more theoretical and more application-oriented concepts. For self-study, we advise our readers to consult complementary introductory material. Chapter 16 lists several textbooks for this purpose. Thanks go to various colleagues and graduate students who most willingly helped with corrections, proofreading, and stylistic improvement, and last but not the least, to the reviewers of the first edition, in particular, to Profs. Gerhard Sessler and Dominique J. Chéenne. Nevertheless, the authors assume full responsibility for all contents. For the current edition, we reversed the authors’ order. Ning Xiang is now the corresponding author, and Jens Blauert acts as the co-author. In this (third) edition, we corrected recognized errors and typos, and edited several figures, notations, and equations to increase the clarity of the presentation. Also, we made some appropriate amendments. At every chapter’s end, we offer exercise problems. Chapter 15 proposes approaches to solving them. The problems provide our readers with the opportunity to explore the underlying mathematical background in more detail. However, the study of the problems and their proposed solutions is no prerequisite for comprehending the material presented in the book’s main body. Troy, NY, USA Bochum, Germany April 2021 Ning Xiang Jens Blauert ix Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Definition of Three Basic Terms . . . . . . . 1.2 Specialized Areas within Acoustics . . . . . 1.3 About the History of Acoustics . . . . . . . . 1.4 Relevant Quantities in Acoustics . . . . . . . 1.5 Some Numerical Examples . . . . . . . . . . . 1.6 Logarithmic Level Ratios and Logarithmic Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Double-Logarithmic Plots . . . . . . . . . . . . 1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 3 4 5 6 ............... ............... ............... 7 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequency 2 Mechanic and Acoustic Oscillations . . . . . . . . . . . . . . . . . . . . 2.1 Basic Elements of Linear, Oscillating, Mechanic Systems 2.2 Parallel Mechanic Oscillators . . . . . . . . . . . . . . . . . . . . . 2.3 Free Oscillations of Parallel Mechanic Oscillators . . . . . . 2.4 Forced Oscillation of Parallel Mechanic Oscillators . . . . . 2.5 Energies and Dissipation Losses . . . . . . . . . . . . . . . . . . 2.6 Basic Elements of Linear, Oscillating, Acoustic Systems . 2.7 The Helmholtz Resonator . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 16 18 19 21 24 25 26 27 3 Electromechanic and Electroacoustic Analogies . . . . . . . . 3.1 The Electromechanic Analogies . . . . . . . . . . . . . . . . 3.2 The Electroacoustic Analogy . . . . . . . . . . . . . . . . . . 3.3 Levers and Transformers . . . . . . . . . . . . . . . . . . . . . 3.4 Rules for Deriving Analog Electric Circuits . . . . . . . 3.5 Synopsis of Electric Analogies of Simple Oscillators . 3.6 Circuit Fidelity, Impedance Fidelity and Duality . . . . 3.7 Examples of Mechanic and Acoustic Oscillators . . . . 3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 32 33 33 35 36 36 38 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . xi xii Contents Electromechanic and Electroacoustic Transduction . . . . . . . . . 4.1 Electromechanic Couplers as Two- or Three-Port Elements 4.2 The Carbon Microphone—A Controlled Coupler . . . . . . . 4.3 Fundamental Equations of Electroacoustic Transducers . . . 4.4 Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Coupling of Electroacoustic Transducers to the Sound Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Pressure and Pressure-Gradient Receivers . . . . . . . . . . . . . 4.7 Further Directional Characteristics . . . . . . . . . . . . . . . . . . 4.8 Absolute Calibration of Transducers . . . . . . . . . . . . . . . . . 4.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 44 45 46 49 . . . . . . . . . . . . . . . 50 52 56 58 59 5 Magnetic-Field Transducers . . . . . . . . . . . . . . . . . . . . . . 5.1 The Magnetodynamic Transduction Principle . . . . . 5.2 Magnetodynamic Sound Emitters and Receivers . . . 5.3 The Electromagnetic Transduction Principle . . . . . . 5.4 Electromagnetic Sound Emitters and Receivers . . . . 5.5 The Magnetostrictive Transduction Principle . . . . . . 5.6 Magnetostrictive Sound Transmitters and Receivers 5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 65 66 73 75 76 77 77 6 Electric-Field Transducers . . . . . . . . . . . . . . . . . . . 6.1 The Piezoelectric Transduction Principle . . . . . 6.2 Piezoelectric Sound Emitters and Receivers . . 6.3 The Electrostrictive Transduction Principle . . . 6.4 Electrostrictive Sound Emitters and Receivers . 6.5 The Dielectric Transduction Principle . . . . . . . 6.6 Dielectric Sound Emitters and Receivers . . . . 6.7 Further Transducer and Coupler Principles . . . 6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 79 82 86 87 87 90 93 94 7 The Wave Equation in Fluids . . . . . . . . . . . . . . . . . . . . . . . 7.1 Derivation of the One-Dimensional Wave Equation . . 7.2 Three-Dimensional Wave Equation in Cartesian Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Solutions of the Wave Equation . . . . . . . . . . . . . . . . 7.4 Field Impedance and Power Transport in Plane Waves 7.5 Transmission-Line Equations and Reflectance . . . . . . . 7.6 The Acoustic Measuring Tube . . . . . . . . . . . . . . . . . . 7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ...... 97 99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 106 108 108 111 113 Horns 8.1 8.2 8.3 . . . . . . . . . . . . . . . . . . . . . . . . 117 118 120 122 4 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and Stepped Ducts . . . . . . . . . . . . . . . . . . . . . . . . Webster’s Differential Equation—The Horn Equation Conical Horns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Horns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents 8.4 8.5 8.6 8.7 xiii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 126 127 130 Spherical Waves, Harmonics, and Line Arrays . . . . . . . 9.1 The Spherical Wave Equation . . . . . . . . . . . . . . . 9.2 Spherical Sound Sources of the First Order . . . . . 9.3 Spherical Harmonics . . . . . . . . . . . . . . . . . . . . . . 9.4 Higher-Order Spherical Sound Sources . . . . . . . . . 9.5 Line Arrays of Monopoles . . . . . . . . . . . . . . . . . . 9.6 Analogies to Fourier Transform in Signal Theory . 9.7 Directional Equivalence of Sources and Receivers . 9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 134 138 140 143 144 146 149 150 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 154 155 156 158 164 166 11 Dissipation, Reflection, Refraction, and Absorption . . . . . 11.1 Dissipation During Sound Propagation in Air . . . . . . 11.2 Sound Propagation in Porous Media . . . . . . . . . . . . . 11.3 Reflection and Refraction . . . . . . . . . . . . . . . . . . . . 11.4 Wall (Surface) Impedance and Degree of Absorption 11.5 Porous Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Resonance Absorbers . . . . . . . . . . . . . . . . . . . . . . . 11.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 169 170 173 174 177 179 182 12 Geometric Acoustics and Diffuse Sound Fields . 12.1 Mirror Sound Sources and Ray Tracing . . 12.2 Flutter Echoes . . . . . . . . . . . . . . . . . . . . . 12.3 Impulse Responses of Rectangular Rooms 12.4 Diffuse Sound Fields . . . . . . . . . . . . . . . . 12.5 Reverberation-Time Formulas . . . . . . . . . 12.6 Application of Diffuse Sound Fields . . . . . 12.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 9 10 Piston 10.1 10.2 10.3 10.4 10.5 10.6 Radiation Impedances and Sound Radiation Steps in the Area Function . . . . . . . . . . . . Stepped Ducts . . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Membranes, Diffraction and Scattering . . . . . The Rayleigh Integral . . . . . . . . . . . . . . . . . . . Fraunhofer’s Approximation . . . . . . . . . . . . . . The Far-Field of Piston Membranes . . . . . . . . . The Near-Field of Piston Membranes . . . . . . . General Remarks on Diffraction and Scattering . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 186 189 191 193 196 199 202 13 Insulation of Air- and Structure-Borne Sound . . . . . . 13.1 Sound in Solids—Structure-Borne Sound . . . . . . 13.2 Radiation of Airborne Sound by Bending Waves 13.3 Sound-Transmission Loss of Single-Leaf Walls . 13.4 Sound-Transmission Loss of Double-Leaf Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 205 207 209 213 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Contents 13.5 13.6 13.7 13.8 The Weighted Sound-Reduction Index . . . . . . . . . . Insulation of Vibrations . . . . . . . . . . . . . . . . . . . . . Insulation of Floors with Regard to Impact Sounds . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 217 220 221 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paths . ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 224 224 229 230 231 238 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 241 249 258 266 279 289 300 308 318 339 349 359 366 380 16 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1 Complex Notation of Sinusoidal Signals . . 16.2 Complex Notation of Power and Intensity 16.3 Supplementary Textbooks for Self Study . 16.4 Letter Symbols, Notations, and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 399 400 402 403 14 Noise 14.1 14.2 14.3 14.4 14.5 14.6 Control—A Survey . . . . . . . . . . . . . . . Origins of Noise . . . . . . . . . . . . . . . . . Radiation of Noise . . . . . . . . . . . . . . . Noise Reduction as a System Problem . Noise Reduction at the Source . . . . . . . Noise Reduction Along the Propagation Exercises . . . . . . . . . . . . . . . . . . . . . . 15 Solutions to the Exercise Problems 15.1 Chapter 1 . . . . . . . . . . . . . . 15.2 Chapter 2 . . . . . . . . . . . . . 15.3 Chapter 3 . . . . . . . . . . . . . . 15.4 Chapter 4 . . . . . . . . . . . . . . 15.5 Chapter 5 . . . . . . . . . . . . . . 15.6 Chapter 6 . . . . . . . . . . . . . . 15.7 Chapter 7 . . . . . . . . . . . . . . 15.8 Chapter 8 . . . . . . . . . . . . . . 15.9 Chapter 9 . . . . . . . . . . . . . . 15.10 Chapter 10 . . . . . . . . . . . . . 15.11 Chapter 11 . . . . . . . . . . . . . 15.12 Chapter 12 . . . . . . . . . . . . . 15.13 Chapter 13 . . . . . . . . . . . . . 15.14 Chapter 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 About the Authors Ning Xiang, Ph.D. is professor of Acoustics and Signal Processing at the Rensselaer Polytechnic Institute (RPI) in Troy, New York. He is the director of RPI’s Program in Architectural Acoustics. Jens Blauert, Dr.-Ing., Dr.-Tech. h.c. is emeritus professor of Acoustics and Electrical Engineering at the Ruhr-University Bochum (RUB) in Bochum, Germany. He is the founder and former director of RUB’s Institute of Communication Acoustics. xv